20.5.8 problem Problem 8

Internal problem ID [3691]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number : Problem 8
Date solved : Monday, January 27, 2025 at 07:55:26 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Riccati]

\begin{align*} \frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

dsolve((1/x-y(x)/(x^2+y(x)^2))+x/(x^2+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\tan \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.237 (sec). Leaf size: 15

DSolve[(1/x-y[x]/(x^2+y[x]^2))+x/(x^2+y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \tan (-\log (x)+c_1) \]